Processing math: 100%

⇦Chinese Physics Letters, 2016, Vol. 33, No. 11, Article code 113201⇨ High-Resolution Rb Two-Photon Transition Spectroscopy by a Femtosecond Frequency Comb via Pulses Control * Yi-Chi Zhang(张一驰), Peng-Rui Fan(范鹏瑞), Jin-Peng Yuan(元晋鹏), Li-Rong Wang(汪丽蓉)**, Lian-Tuan Xiao(肖连团), Suo-Tang Jia(贾锁堂) Affiliations State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006 Received 25 August 2016 ^*Supported by the National Basic Research Program of China under Grant No 2012CB921603, the Program for Changjiang Scholars and Innovative Research Team in University of Ministry of Education of China under Grant No IRT13076, and the National Natural Science Foundation of China under Grant Nos 61378049, 10934004, 11404198, 61575116 and 61505100.
^**Corresponding author. Email: wlr@sxu.edu.cn Citation Text: Zhang Y C, Fan P R, Yuan J P, Wang L R and Xiao L T et al 2016 Chin. Phys. Lett. 33 113201 Abstract We experimentally observe the high resolution direct frequency comb spectroscopy using counter-propagating broadband femtosecond pulses on two-photon transitions in room-temperature

$^{87}$ Rb atoms. The Doppler broadened background is effectively eliminated with the pulse shaping method and the spectrum modulation technique. The combination of the pulse shaping method and the spectra modulation technique provides a potential approach to reduce background of at least 99%. DOI:10.1088/0256-307X/33/11/113201 PACS:32.10.Fn, 32.50.+d, 34.10.+x © 2016 Chinese Physics Society Article Text The research of high resolution spectroscopy is a very important field in physics. It promotes development of atomic and molecular physics, optoelectronics, extreme ultraviolet (XUV) spectroscopy,[1] and so on, and it also has great significance in the physical chemistry.[2] A variety of techniques have been implemented to eliminate the Doppler effects in optical frequency measurements of atomic transitions. These include saturated absorption spectroscopy in vapor cells,[3,4] magneto-optic traps,[5] thermal atomic beams,[6,7] and two-photon spectroscopy in vapor cells.[8,9] The two-photon spectroscopy experiments in vapor cells are not only easy to perform but also precise. The two-photon excitation is a widely exploited nonlinear phenomenon with applications that extend to the fields of high resolution spectroscopy. In atomic and molecular spectroscopy, because two-photon selection rules are different from one-photon selection rules, two-photon transitions may allow access to states which otherwise could not be reached. Furthermore, parts of the energy spectrum where laser radiation is hardly available may be explored. Direct frequency comb spectroscopy (DFCS) is used to conduct the two-photon transitions (TPTs) in Rb for a higher resolution.[10-12] High resolution may be achieved in TPT DFCS because the spectrum of the comb is composed of narrow evenly spaced lines. Furthermore, the comb has two independent degrees of freedom, it is always possible to simultaneously satisfy two-photon as well as one-photon resonance conditions. DFCS has been performed on the

$5S$ –

$5D$ two-photon transitions in

$^{87}$ Rb, permitting high-resolution spectroscopy of all transitions within the comb bandwidth. In two-photon transitions DFCS driven by using counterpropagating broadband femtosecond comb pulses has two different schemes which decide the spectroscopy simultaneously. The one scheme is stepwise two-photon transitions (S-TPTs) adopting stepwise excitation by two different frequency lasers which drive through real intermediate level and enhances the signal strength.[8,13] The other scheme is direct two-photon transitions (D-TPTs) by using single frequency laser through virtual intermediate level.[14,15] In this Letter, a high-precision D-TPT DFCS in a hot Rb atomic vapor is performed by using broadband femtosecond comb pulse shape and the spectra modulation technique. We use a robust broadband femtosecond comb pulse shape technique to eliminate S-TPT and copropagating D-TPTs. This simple and flexible pulse shaping method can eliminate the Doppler broadened background. Combined with the spectra modulation technique, we enhanced the signal strength of the counterpropagating D-TPT DFCS at the same time. The signals of excellent signal-to-noise ratio (SNR) and lower sensitivity to systematic effects are obtained. The experiment setup is illustrated in Fig. 1. The sample of Rb atoms was prepared in a Brewster window Rb vapor cell (20 mm in diameter and 75 mm in length) at room temperature. The Rb cell is surrounded by

$\mu$ -metal to avoid the perturbation of external magnetic fields. The Rb vapor cell contains natural Rb isotopes (28%

$^{87}$ Rb and 72%

$^{85}$ Rb) and is heated to

$\approx$ 343 K, which is required to obtain a reasonable SNR ratio in the TPT spectroscopy. The entire system setup consists of an optical Er:fiber based on OFC and the pulse shaping part. The OFC laser is a commercial system from a MenloSystems FC1500 optical frequency synthesizer. This OFC is based on a passive mode-locked fiber femtosecond laser centered at 1550 nm, which has a repetition rate about 250 MHz. The repetition rate

$f_{\rm rep}$ of the OFC is phase-locked to a reference signal from a cesium atomic clock via a global positioning system and the carrier-offset-envelope frequency

$f_{0}$ is phase-locked to the same cesium atomic clock by the well-known

$f$ –2

$f$ self-referencing technique.[11] The Er:fiber OFC has a two-branch-type configuration. One part of this OFC output is amplified by an erbium-doped fiber amplifier (EDFA) and is spectrally broadened to the wavelength range from 1050 to 2100 nm by using a highly nonlinear fiber (HNF) to stabilize

$f_{0}$ . The other part of the OFC output is amplified by other EDFA and is frequency doubled by a periodically poled lithium niobate (PPLN) crystal. Then, this part of the laser is spectrally broadened by a photonic crystal fiber (PCF) to cover the wavelength range from 600 to 900 nm. All synthesizers and counters are referenced to a 10-MHz signal from a GPS-disciplined, ultrastable quartz oscillator (TimeTech Reference Generator) with relative stability better than

$5\times10^{-12}$ in 1 s.[12] The frequency of the

$n$ th tooth is given by

$f=f_{0}+nf_{\rm rep}$ . The relevant hyperfine structure energy levels of Rb in this experiment are shown in the inset of Fig. 1.

Fig. 1. (a) Experimental setup of the two-photon transitions. MS:

$\mu$ -metal sheet; HT: heating tape; PMT: photomultiplier tube; PPLN: periodically poled lithium niobate; PCF: photonic crystal fiber; and BB: black block. (b) Pulse control scheme in the D-TPTs.

The transitions are induced by focusing shaped 778 nm pulses in the center of the cell with

$f=10$ cm convex lens to a beam size of about 80 μm at the focus. A mirror reflects the pulses back so that pulses overlap at the focus. Two-photon resonance signals were monitored by measuring 6

$P_{3/2}\to6$

$S_{1/2}$ spontaneous fluorescence at 420 nm. The fluorescence collected by a convex lens at a right angle to the counter-propagating beams was detected by using a photomultiplier tube (PMT). The detector avoided background light and chose the light from the excitation laser beams by a 420 nm filter with a 10 nm pass band. In this study, the TPT DFCS is performed by sweeping repetition rate

$f_{\rm rep}$ of the OFC. In this work, we block

$<$ 777 nm and

$>$ 779 nm broadband femtosecond comb pulses to eliminate S-TPTs using two black blocks (BBs) as shown in Fig. 1(a). Copropagating D-TPTs play the dominate role in generating Doppler-broadening background. We use group delay zero-dispersion 2

$f--$ 2

$f$ configuration to eliminate copropagating D-TPTs, as shown in Fig. 1. This group delay induced the time delay between different frequency pulses that will remove the copropagating signals. The 99% of the Doppler-broadening background are eliminated by using this pulse shaping method. The pure counterpropagating D-TPTs are chosen to achieve high precision DFCS. The counterpropagating D-TPT DFCS has weak signal strength caused by excitation through the virtual intermediate level. We use the spectra modulation technique to enhance the signal strength. The laser beam passes through a chopper wheel which modulates the light at sine function. For sine wave modulation, the instantaneous frequency of the coupling laser is

$v(t)=v_{0}-m\cos(2\pi \omega t)$ , where

$v_{0}$ is the carrier frequency,

$m$ is the modulation index, and

$\omega$ is the modulation frequency. We apply the optimal values of modulation index and frequency,

$m=2$ and

$\omega=200$ Hz. We take first-order

$\omega$ as the demodulation reference frequency.[13] The spectra modulation technique is used to enhance the counter propagating D-TPT DFCS SNR up to 400, as shown in Fig. 2(b).

Fig. 2. Variation of the spectrum with

$f_{\rm rep}$ scanned around 250 MHz. (a) The spectrum for the 5

$S_{1/2}\to 5P_{3/2}\to 5D_{5/2}$ TPTs for

$^{87}$ Rb atoms without modulation. (b) The spectrum for the 5

$S_{1/2}\to 5P_{3/2}\to 5D_{5/2}$ transitions for

$^{87}$ Rb atoms with modulation index and frequency,

$m=2$ and

$\omega=200$ Hz.

In experiment, we recorded the fluorescence signals by scanning the repeat rate of frequency combs

$f_{\rm rep}$ to obtain the TPT-DFCS of

$^{87}$ Rb. The scanning speed of

$f_{\rm rep}$ is 1 Hz/s, corresponding to the optical frequency scanning speed of

$\sim$ 3 MHz/s at 780 nm. The fluorescence signals from the PMT were recorded by an oscilloscope. We could obtain the

$^{87}$ Rb TPT signals in a single scan process, as shown in Fig. 3. The Doppler-free TPTs take place when the frequency of either one OFC tooth or the center of two adjacent OFC teeth is equal to the TPT frequency. D-TPTs and S-TPTs have different physics schemes. The S-TPTs are a stepwise scheme. In this scheme, two tooth pulses arrive at the atom at different times to excite the two-step S-TPTs, in which we must ensure that atoms have not decayed to the ground

$5S$ state before being excited to the

$5D$ state.

Fig. 3. TPT spectrum for the 5

$S_{1/2}\to 5P_{3/2}\to 5D_{5/2}$ of

$^{87}$ Rb atoms. Variation of the TPTs with

$f_{\rm rep}$ scanned around 250 MHz. The contribution of D-TPTs performs a constant background. The blue bars demonstrate the calculated strengths and positions of the resonant D-TPT lines.

The sum frequency of two comb lines should be equal to the

$5S$ –

$5D$ transition frequency, for example,

$F_{\rm t}=F_{\rm teeth1}+F_{\rm teeth2}$ . Then, we obtained the result free from Doppler broadening signals. However, due to the atoms transfer to the intermediate state, the systematic effects are complicated. In this scheme, the Doppler-free excitation occurs in the whole optical path. The line center is shifted due to the imbalance between the two comb teeth. On the other hand, the Rb atom absorbs two photons at the same time and is excited directly from the

$5S$ state to

$5D$ state in the scheme of D-TPTs. Two photons provided by the same comb teeth should reach the atom in the meantime. The double frequency of one comb line should be equal to the

$5S$ –

$5D$ transition frequency, for example,

$F_{\rm t}=2F_{\rm teeth1}$ . In this scheme, the Doppler-free excitation occurs just in the region of the laser path where the counterpropagating pulses overlap. Because comb pulses duration is in the femtosecond region, the overlap is just tens of micrometers. The systematic effects and the line center shift are tiny in D-TPTs. To obtain the high precision TPT spectrum, we obtain D-TPTs in this work. In D-TPTs, counterpropagating TPTs occur in tens of micrometers, to be TPTs signal. In contrast, counterpropagating TPTs occur over the whole beam path which only provides background noise. The D-TPTs background is almost 20% in all signals. In this work, we use the 2

$f$ -pulse delay system to cancel the counterpropagating TPT noise, as shown in Fig. 1(b). With the combination of the pulse control and spectrum modulation techniques we can eliminate the D-TPTs background, as shown in Fig. 4. The Doppler-free TPT spectrum for the 5

$S_{1/2}\to 5P_{3/2}\to 5D_{5/2}$ of

$^{87}$ Rb atoms performs a linewidth about 3 MHz, which is larger than the natural linewidth (

$\sim$ 300 kHz). The linewidth broadening is due to the laser power broadening, residual Doppler broadening, and transit time broadening.

Fig. 4. Doppler-free TPT spectrum for the 5

$S_{1/2}\to 5P_{3/2}\to 5D_{5/2}$ of

$^{87}$ Rb atoms. The blue bars demonstrate the calculated strengths and positions of the resonant D-TPT lines.

In conclusion, we have demonstrated the

$^{87}$ Rb 5

$S_{1/2}\to 5P_{3/2}\to 5D_{5/2}$ TPT spectrum by group delay zero-dispersion 2

$f--$ 2

$f$ configuration pulses control and spectra modulation techniques to eliminate copropagating D-TPTs, and 99% of Doppler-broadening background is eliminated by using this pulse control method. The signals of excellent SNR and lower sensitivity to systematic effects are obtained. The narrow linewidth

$\sim$ 3 MHz of spectrum is obtained. These techniques will further apply in nonlinear spectroscopy, microscopy and high-precision frequency metrology. References Direct frequency comb spectroscopy in the extreme ultravioletPhysical chemistry: Combs for moleculesAbsolute optical frequency measurement of the cesium

$D_{2}$ lineHyperfine structure and absolute frequency of the ^87Rb 5P_3/2 stateOptical frequency standard based on cold ca atomsAbsolute Frequency Measurements of the

$2^{3} S_{1} \to 2^{3} P_{0, 1, 2}$ Atomic Helium Transitions around 1083 nmPrecision Frequency Measurement of Visible Intercombination Lines of StrontiumLine shape and strength of two-photon absorption in an atomic vapor with a resonant or nearly resonant intermediate stateMeasurement of the Fine-Structure Splitting of the

$4 F$ State in Atomic Sodium Using Two-Photon Spectroscopy with a Resonant Intermediate StateChirped-pulse direct frequency-comb spectroscopy of two-photon transitionsErbium fiber laser-based direct frequency comb spectroscopy of Rb two-photon transitionsExperimental Measurement of the Absolute Frequencies and Hyperfine Coupling Constants of ¹³³ Cs Using a Femtosecond Optical Frequency CombFemtosecond frequency comb measurement of absolute frequencies and hyperfine coupling constants in cesium vaporHigh-Precision Spectroscopy with Counterpropagating Femtosecond PulsesTwo-photon spectrum of ⁸⁷ Rb using optical frequency comb

[1]	Cingöz A, Yost D C, Allision T K, Ruehl A, Fermann M E, Hartl I and Ye J 2012 Nature 482 68
[2]	Siberberg Y 2013 Nature 502 307
[3]	Udem T, Reichert J, Hansch T W and Kourogi M 2000 Phys. Rev. A 62 031801
[4]	Ye J, Swartz S, Jungner P and Hall J L 1996 Opt. Lett. 21 1280
[5]	Helmcke J, Wilpers G, Binnewies T et al 2003 IEEE Trans. Instrum. Meas. 52 250
[6]	Pastor P C, Giusfredi G and Natale P D 2004 Phys. Rev. Lett. 92 023001
[7]	Ferrari G, Cancio P, Drullinger R, Giusfredi G, Poli N, Prevedelli M, Toninelli C and Tino G M 2003 Phys. Rev. Lett. 91 243002
[8]	Bjorkholm J E and Liao P F 1976 Phys. Rev. A 14 751
[9]	Liao P F and Bjorkholm J E 1976 Phys. Rev. Lett. 36 1543
[10]	Peer A, Shapiro E A, Stowe M C, Shapiro M and Ye J 2012 Phys. Rev. A 86 022514
[11]	Wu J T, Hou D, Qin Z Y, Dai X L Zhang Z G and Zhao J Y 2013 Opt. Lett. 38 5028
[12]	Jin L, Zhang Y C, Xiang S S, Wang L R, Ma J, Zhao Y T, Xiao L T and Jia S T 2013 Chin. Phys. Lett. 30 103201
[13]	Stalnaker J E, Mbele V, Gerginov V, Fortier T M, Diddams S A, Hollberg L and Tanner C E 2010 Phys. Rev. A 81 043840
[14]	Barmes I, Witte S and Eikema K S E 2013 Phys. Rev. Lett. 111 023007
[15]	Wang L R, Zhang Y C, Xiang S S, Cao S K, Xiao L T and Jia S T 2015 Chin. Phys. B 24 063201